A device for cutting a web of material comprises movement means for moving a web of material to be cut, defining a feed path for the web at least partly rotatable about a central axis and equipped with at least one conveyor mounted around the central axis, at least one cutting head equipped with a laser source and an optical system configured to direct the laser beam towards a cutting zone, where the optical system of the cutting head comprises at least one directing member located inside the conveyor to direct the laser beam away from the central axis towards the cutting zone.